A brief overview of phased arrays is provided in this section in a context which illustrates system requirements and existing implementations. In this section, we will focus primarily on the receiver, though the concepts described also can be applied to the transmitter.
Phased arrays are used to electronically steer the direction of maximum sensitivity of a receiver, providing spatial selectivity or equivalently higher antenna gain. Phased arrays find use in many different wireless applications, including but not limited to RADAR and data communications. Beam steering is achieved by first shifting the phase of each received signal by progressive amounts to compensate for the successive differences amongst arrival phases. These signals are then combined, where the signals add constructively for the desired direction and destructively for other directions.
FIG. 1 shows a block diagram of a conventional linear phased array receiver 100 combined at radio frequency (RF) having N elements, where N=4. The antennas (102-0 through 102-3) are spaced apart by a distance, d, and are situated along the z-axis. Using the spherical coordinate system, a signal arriving at the nth element in the array with an angle of incidence, θ, will experience a phase shift, ψn, of:ψn=−nkd cos(θ)=−nψo,  (1)where k is the phase velocity, equal to 2π/λ, with λ the wavelength. Phase shifters (104-0 through 104-3) in the receive elements add a compensating delay equal to (N−n)α. Combining the outputs of all of the parallel receivers via combiner 106, the resultant signal in phasor notation is:
                                                        I              =                            ⁢                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      I                    n                                    ⁢                                      ⅇ                                          j                      ⁡                                              [                                                                              ψ                            n                                                    -                                                                                    (                                                              N                                -                                n                                                            )                                                        ⁢                            α                                                                          ]                                                                                                                                                                    =                            ⁢                                                I                  o                                ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    α                                                  ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                            ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                                                  n                          ⁡                                                      [                                                                                          kd                                ⁢                                                                                                                                  ⁢                                                                  cos                                  ⁡                                                                      (                                    θ                                    )                                                                                                                              -                              α                                                        ]                                                                                                                .                                                                                                          (        2        )            Currents are used in this equation, though other metrics could be used. It can be shown that the angle of maximum sensitivity, θmax, occurs at:
                                                                        θ                max                            =                            ⁢                                                arccos                  ⁡                                      (                                          α                      kd                                        )                                                  ⁢                                  |                                      d                    =                                          λ                      /                      2                                                                                                                                                              =                                ⁢                                                      arc                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              (                                                  α                          π                                                )                                                                              |                                            ,                                                          (        3        )            which is where kdcos(θmax)=α; hence, α is used to steer the beam. At θmax, the currents add in phase to a resultant value which is N times as large as each individual current. This results in an N2 increase in the received power level.
Since there are now N receive elements generating uncorrelated noise, the total noise power is N times as large (variances add); hence, the received signal-to-noise ratio is increased by a factor of N. Another useful metric for phased arrays is the directivity, which is the ratio of the maximum radiated power to that from an isotropic radiator. This can also be shown to be N; thus, higher directivity requires more elements in the phased array.
From these equations, some basic system requirements can be derived. First, assume that the antennas are spaced a half-wavelength apart, making kd=π. Such a spacing eliminates the presence of grating lobes. For a four-element linear array example with θ=0, then ψo=π and the incident phases at each receiving antenna are (0, −π, −2π, −3π). The required phase shifts in each phase shifter are then (αmin−3π, αmin−2π, αmin−π, αmin), where αmin is the minimum possible phase shift through the device. At θ=π/2, ψo=0 and the incident phases at the antennas are (0, 0, 0, 0). The required phase shifts through the phase shifters are all equal to αmin. These two cases define the range of required phase shifts in each element, which is αmin to αmin−3π. More generally, for an N-element array, the phase shifter has to vary from αmin to αmin−N−1)π. Such a large phase-shift range can be difficult to achieve.
A second system requirement comes from the insertion loss of the phase shifters. This amounts to a substitution of k=β−jα, where α is the loss per unit length, into equation (2), resulting in an exponentially decreasing term within the summation. For coherent signal addition, amplifiers must be inserted to equalize the varying signal amplitudes. Without these amplifiers, the directivity of the array will suffer.
The above example was for an RF-combined phased array. It is possible, though, to combine the signals at any point in the received signal path, such as at the intermediate frequency (IF), the baseband frequency, or even in the digital domain. Each has its own advantages and disadvantages. Comparing the two extremes—RF combining and digital combining—one finds that RF combining results in the lowest power consumption and required area. This comes with the penalty of having to generate very precise phase shifts and amplitude balance at high frequencies. On the other hand, digital combining (also known as digital beamforming) has the advantage of being able to generate very accurate phase shifts and amplitude balance, within the accuracy of the analog-to-digital converter (ADC). The key drawback of digital beamforming is the need for complete parallel receivers all feeding a single ADC. For very high data rates, this ADC can be quite complex. Hence, digital beamforming can be area and power intensive.
Another option for phased arrays is to combine at IF, after the mixer. It should be realized that the phase shift for the signals can then be realized in either the signal path or the local oscillator (LO) path. Multiple phases of the LO signal can be generated globally or locally, and these different phases can be used to provide the necessary phase shift to the array elements. This has the benefit of being able to match the amplitudes much better, since lossy phase shifters in the signal path are not needed. A drawback of this approach, though, is that the LO generation and distribution circuitry can consume sizeable power and/or area. Also, such an approach can suffer from mixer nonlinearity, where blocking signals located outside of the desired direction still make it to the mixer since they have not yet been cancelled at that point.